Sine-Gordon multisoliton form factors in finite volume

Self Cite

We study the finite-temperature expectation values of exponential fields in the sine-Gordon model. Using finite-volume regularization, we give a low-temperature expansion of such quantities in terms of the connected diagonal matrix elements, for which we provide explicit formulas. For special values of the exponent, computations by other methods are available and used to validate our findings. Our results can also be interpreted as a further support for a previous conjecture about the connection between finite-and infinite-volume form factors valid up to terms exponentially decaying in the volume.

Section: One-point Functions At Finite Temperaturementioning

confidence: 99%

“…as noted in [21]. This is due to a difference in the conventions of the form factor equation, which corresponds to a redefinition of relative phases of the multi-particle states [21].…”

Section: Form Factors Of Exponential Fieldsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Finite temperature one-point functions in non-diagonal integrable field theories: the sine-Gordon model

Buccheri

Takács

2014

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“…This is why it would be interesting to test the conjecture for such operators, which do not belong to the conserved quantities of the model. The results of [7,8] indicate that the truncated conformal space approach could be an appropriate method for such investigations.…”

Section: Summary Outlook and Discussionmentioning

confidence: 99%

“…In the past decade a remarkable progress has been made in the computation of finite volume form factors in integrable quantum field theories [4][5][6][7][8][9][10][11]. Most of the methods use the infinite volume form factors [12] as a starting point and the finite volume form factors are to be determined in the form of a systematic large volume series.…”

Section: Introductionmentioning

confidence: 99%

Exact finite volume expectation values of $$ \overline{\varPsi}\varPsi $$ in the massive Thirring model from light-cone lattice correlators

Hegedűs

2018

In this paper, using the light-cone lattice regularization, we compute the finite volume expectation values of the composite operatorΨΨ between pure fermion states in the Massive Thirring Model. In the light-cone regularized picture, this expectation value is related to 2-point functions of lattice spin operators being located at neighboring sites of the lattice. The operatorΨΨ is proportional to the trace of the stress-energy tensor. This is why the continuum finite volume expectation values can be computed also from the set of non-linear integral equations (NLIE) governing the finite volume spectrum of the theory. Our results for the expectation values coming from the computation of lattice correlators agree with those of the NLIE computations. Previous conjectures for the LeClair-Mussardotype series representation of the expectation values are also checked.

Exact finite volume expectation values of local operators in excited states

Pozsgay¹,

Szécsényi

Takács

2015

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We present a conjecture for the exact expression of finite volume expectation values in excited states in integrable quantum field theories, which is an extension of an earlier conjecture to the case of general diagonal factorized scattering with bound states and a nontrivial bootstrap structure. The conjectured expression is a spectral expansion which uses the exact form factors and the excited state thermodynamic Bethe Ansatz as building blocks. The conjecture is proven for the case of the trace of the energy-moment tensor. Concerning its validity for more general operators, we provide numerical evidence using the truncated conformal space approach. It is found that the expansion fails to be well-defined for small values of the volume in cases when the singularity structure of the TBA equations undergoes a non-trivial rearrangement under some critical value of the volume. Despite these shortcomings, the conjectured expression is expected to be valid for all volumes for most of the excited states, and as an expansion above the critical volume for the rest.